Let be a continuous function on the closed interval .

MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

Let

g

be a continuous function on the closed interval

[2,6]

. (1) Write an expression for the average value of

g

on the interval

[2,6]

. (2) Explain why there must exist at least one number

c

[2,6]

such that

g(c)

equals the average value obtained in part (a). Your explanation should rely only on properties of continuous functions on closed intervals.